In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron [math]\displaystyle{ P }[/math] and a vector [math]\displaystyle{ \mathbf{x}^* \in \mathbb{R}^n }[/math], [math]\displaystyle{ \mathbf{x}^* }[/math] is a basic solution if:
A constraint is active for a particular solution [math]\displaystyle{ \mathbf{x} }[/math] if it is satisfied at equality for that solution.
A basic solution that satisfies all the constraints defining [math]\displaystyle{ P }[/math] (or, in other words, one that lies within [math]\displaystyle{ P }[/math]) is called a basic feasible solution.
Original source: https://en.wikipedia.org/wiki/Basic solution (linear programming).
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